Unlike the real line, the real space, in dimension d≥ 2, is not canonically ordered. As a
consequence, extending to a multivariate context fundamental univariate statistical tools …

Distribution and quantile functions, ranks and signs in dimension d: A measure
transportation approach Page 1 The Annals of Statistics 2021, Vol. 49, No. 2, 1139–1165 …

Modern Directional Statistics collects important advances in methodology and theory for
directional statistics over the last two decades. It provides a detailed overview and analysis …

Monge-Kantorovich depth, quantiles, ranks and signs Page 1 The Annals of Statistics 2017,
Vol. 45, No. 1, 223–256 DOI: 10.1214/16-AOS1450 © Institute of Mathematical Statistics …

We introduce directional regression (DR) as a method for dimension reduction. Like contour
regression, DR is derived from empirical directions, but achieves higher accuracy and …

This article investigates the problem of testing independence of two random vectors of
general dimensions. For this, we give for the first time a distribution-free consistent test. Our …

Robust statistical methods were developed to supplement the classical procedures when
the data violate classical assumptions. They are ideally suited to applied research across a …

Multivariate nonparametric statistical tests of hypotheses are described for the one-sample
location problem, the several-sample location problem and the problem of testing …

Extending rank-based inference to a multivariate setting such as multiple-output regression
or MANOVA with unspecified d-dimensional error density has remained an open problem for …

We propose a class of rank-based procedures for testing that the shape matrix V of an
elliptical distribution (with unspecified center of symmetry, scale and radial density) has …